Ok, here goes...
Raise preflop - This is a bad play. 2 x BB in a NL cash game, especially with the blinds this low is asking for trouble. You should be making a minimum 4 x BB raise, not 2. This would have definitely pushed out the BB, who has every right to call with low suited cards
The flop - You make a terribly weak bet here. This flop should not be scaring you at all, or it wouldnt normally as it is unlikely anyone holding a 6 will not call a 4 x BB raise. Then you come into a raise - raise situation, and this must be seriously worrying you. Also you are out of position, meaning you will be first to act on the turn and river and you gotta be asking yourself "I am willing to call bets on the turn and river when I dont have a clue where I am in the hand?"
The turn - You are making a weak bet here, hoping to only get called and to see a free card on the river. At best I am checking
The river - You could easily have lost more, as the guy with 6's should really be raising into you
I think you fell into the trap of being 'married' to your hand and didnt wanna lay it down. QQ is very nice, particularly in NL but you should be worried when drawing to only 2 outs and calling down
Review the hand again yourself and ask yourself what your opponents would be raising with, as you lose to any player holding a 6, 88, KK and AA